OPTIMAL RELAXED CONTROL OF DISSIPATIVE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN BANACH SPACES

被引：18
|
作者：
Brzezniak, Zdzislaw [1 ]
Serrano, Rafael [2 ]
机构：
[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
[2] Univ Rosario, Fac Econ, Bogota, Colombia
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 03期
关键词：
relaxed control; stochastic PDE; multiplicative cylindrical noise; stochastic convolution; UMD type-2 Banach spaces; Young measures; Suslin control set; EVOLUTION-EQUATIONS; EXPONENTIAL ERGODICITY; PARABOLIC EQUATIONS; EXISTENCE; RELAXATION; CONVERGENCE; POWERS;
D O I：
10.1137/100788574
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrizable control sets.
引用
收藏
页码：2664 / 2703
页数：40
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